Linear 0-1 Inequalities and Extended Clauses

Extended clauses are the basic formulas of the 0-1 constraint solver used in the constraint logic programming language CLP($\cal PB$). We present a method for transforming an arbitrary linear 0-1 inequality into a set of extended clauses, such that the solution space remains invariant. The method relies on cutting planes techniques known from integer programming. We develop special redundancy criteria and can so produce the minimal number of extended clauses. We show how the algorithm can be used to replace the resolution rule in the generalized resolution algorithm for extended clauses. Furthermore the method can be used to obtain all strongest extended cover inequalities of a knapsack inequality